ROBUST MULTI-OBJECTIVE SINGULAR OPTIMAL CONTROL OF PENICILLIN FERMENTATION PROCESS

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. This singular problem is very difficult to solve due to nonlinear dynamics of system model, the presence of control variable in linear form and the existence of constraints on both the state and control variables. Traditionally, during the optimization process no uncertainty associated to design variables, parameters and mathematical model is considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi-objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time. In order to implement a point
of Pareto’s Curve obtained, the overall profit is considered as a post-processing criterion. The results obtained indicate that the proposed methodology is configured as an interesting approach to solve this kind of problem.